We present measurements of microwave-induced Shapiro steps in a superconducting nanobridge weak link in the dissipative branch of a hysteretic current-voltage characteristic. We demonstrate that Shapiro steps can be used to infer a reduced critical current and an associated local temperature. Our observation of Shapiro steps in the dissipative branch shows that a finite Josephson coupling exists in the dissipative state. Although the nanobridge is heated, our model shows that the temperature remains below the critical temperature. This work provides evidence that Josephson behavior can still exist in thermally hysteretic weak-link devices and will allow extension of the temperature range over which nanobridge-based single-flux-quantum circuits, micron-sized superconducting quantum interference devices (i.e., nanoSQUIDs), and Josephson voltage standards can be used.
The quantum system associated with a resistor-shunted weak-link junction circuit may be described in terms of a single Lagrangian. In this representation the degrees of freedom internal to the dissipative energy of the resistor can be systematically separated from the Hamiltonian formulation of the circuit. This allows us to solve the quantum states of the junction while the effects of the resistor on the circuit are included as a Lagrangian multiplier. In this manner the effects of the measuring apparatus or resistor on the quantum state of the junction may be calculable. The calculations are in very good agreement with experiments.
Superconducting qubits are among the most promising platforms for realizing practical quantum computers. One requirement to create a quantum processor is nonlinearity, which in superconducting circuits is typically achieved by sandwiching a layer of aluminum oxide between two aluminum electrodes to form a Josephson junction. These junctions, however, face several limitations that hinder their scalability: the small superconducting gap of aluminum necessitates millikelvin operating temperatures, the material interfaces lead to dissipation, and the sandwich geometry adds unwelcome capacitance for high-frequency applications. In this work, we address all three limitations using a novel superconducting weak link based on the superconductor-insulator transition. By locally thinning a single film of niobium nitride, we exploit its thickness-driven superconductor-insulator transition to form a weak link employing only atomic layer deposition and atomic layer etching. We utilize our weak links to produce a transmon qubit, '
planaron', with a measured anharmonicity of
α/2π=235 MHz; at present, the linewidth is
κ/2π=15MHz. The high superconducting gap of niobium nitride can enable operation at elevated temperatures in future devices, and the fully planar geometry of the weak link eliminates superfluous material interfaces and capacitances. The investigation of small patches of material near the SIT can shed new light on the nature of the transition, including the role of dissipation and finite-size effects.